A Pipeline From COLLADA to WebGL for Skeletal Animation

Transcription

1 A Pipeline From COLLADA to WebGL for Skeletal Animation Jeffery McRiffey, Ralph M. Butler, and Chrisila C. Pettey Computer Science Department, Middle Tennessee State University, Murfreesboro, TN, USA Abstract - Effective use of HTML5's canvas and its access to WebGL for rendering 3D content requires knowledge of how to import externally developed 3D content. Additionally, in order to efficiently reuse 3D content in various different browser applications, it is convenient to have a data format that can be rendered directly by the JavaScript program with WebGL. To that end, we have provided a process for extracting data from COLLADA files using Python's elementtree, storing it in a JSON format, and rendering it with JavaScript and WebGL. This process works for skeletal animation as well as other, less complicated, 3D data. Keywords: WebGL, COLLADA, Skeletal Animation, Maya, HTML5 In this paper we show how the power of Python's elementtree can be used to extract skeletal animation data from a COLLADA file converting it to a JSON format that can be rendered by WebGL. We begin with a discussion of the data that is needed by showing an example JSON file. We then show where the data can be found in a COLLADA file and how it can be extracted with Python's elementtree. We end with an explanation of how to render the JSON data with JavaScript and WebGL. Figures 1 and 2 show examples of screenshots of skeletal animation done with the process described in this paper. However, these two examples contain more triangles and joints than can be easily described here. Therefore, we will use the example shown in Figure 3 of a cube with nine joints where joints 3 and 4 are animated. 1 Introduction In the past, browser-based 3D graphics have been dependent on cumbersome plug-ins that were deficient in customization, sometimes relied on less efficient softwarebased rendering, required frequent plug-in related updates, and lacked support for mobile systems [3]. HTML5's canvas and its access to WebGL overcome these deficiencies. However, effective use of these technologies requires knowledge of how to import externally developed 3D content. For static geometry this process is fairly straightforward. The real challenge comes with rendering of skeletal animation. Our goal was to get a 3D object into our existing engine without altering the game engine code so that it could parse 3D files. To do this we decided to develop an external utility that would create an intermediate file using the JSON format. This would allow us to keep the game engine small, and at the same time allow us to investigate what data needed to be extracted. There are several file formats for 3D objects (e.g., dae, fbx, and obj). Since dae seemed to be an industry standard, we started with that. However, the interpretations of the standard were inconsistent (for example we could not move dae files between Blender and Maya). Since the standard was hard to interpret, we looked for software to help us. Surprisingly, at the time we began this, all the software that existed only dealt with static geometry. There were some packages that could understand animations for instance Maya can import a dae file but for the most part these were proprietary and did not export the file in a format that we could use. Figure 1. Three frames of a hand opening animation Figure 2. Three frames of a human jumping animation Figure 3. Three frames of an animated cube

2 2 Required data in JSON format The JSON format is a text based standard used for efficient information serialization and transmission [8]. Specifically, JSON is space efficient and eliminates the need for parsing COLLADA files within the rendering engine. The organization of the final JSON file is a series of key-value pairs. Figure 4 shows a subset of the JSON file for the animated cube shown in Figure 3. All 3D models have vertices that have positions, normals, and texture coordinates. The three attributes POSITION, NORMAL, and TEXCOORD can be seen as keys in Figure 4. The actual floating point values for the vertex attributes are stored in large arrays (represented as the values [] in Figure 4). Since each vertex has three values for position, three values for normal, and two values for texture coordinate, each vertex has eight numbers associated with it. Additionally all meshes are ultimately represented as triangles because that is currently required by WebGL. Since a vertex can belong to multiple triangles, the triangles are represented by an array of indices (another key-value pair with INDEX as the key). The key-value pairs directly related to animation are: JOINT_ID (a list of the joint names), WEIGHT (a list of joints that affect each vertex), BIND_SHAPE_MATRIX (a 4x4 matrix that allows for the mesh to be transformed by the skeleton s coordinate system [2]), JOINT (a description of each joint including the joint's id, parent, and the two 4X4 bind pose and inverse bind pose matrices), and ANIMATION (a dictionary containing a 4X4 matrix for each frame for each joint). 3 COLLADA COLLADA is an open, XML-based 3D asset format maintained by the Khronos Group [5]. There are a few comments that need to be made about creating the COLLADA files. First, all geometry should be triangulated before exporting because WebGL requires it [3]. Second, all animations should be baked before exporting as COLLADA. Finally, it is necessary to export the transformations as a single matrix (i.e., scale, rotation, and translation information is a single 4X4 matrix for all transformed portions of the model). To produce the appropriate JSON file we need to scan a COLLADA file for tags that define the elements associated with the JSON keys that were described in the preceding section. This sounds like an easy task, however COLLADA files are typically very large and the data for a single element is scattered throughout the tree hierarchy, sometimes with logical pointers from one portion of the tree into another. In the remainder of this section we will briefly describe the location of the various necessary elements within a Maya generated dae file. While all 3D content packages do produce dae files that conform to the standard, they do not typically produce the same dae file. So we concentrated on dae files produced by Maya. model = "Cube": "POSITION": [ ], "NORMAL": [ ], "TEXCOORD": [ ], "WEIGHT": [ ], "JOINT_ID": [ ], "INDEX": [ ], "BIND_SHAPE_MATRIX": [ ], "IMAGE_LOCATION": "textures/box.jpg", "JOINT": "joint1": "ID": 0,"PARENT": -1,"BIND_POSE": [ ],"INVERSE_BIND_POSE": [ ], "joint2": "ID": 1,"PARENT": joint1,"bind_pose": [ ],"INVERSE_BIND_POSE": [ ], "joint8": "ID": 7,"PARENT": joint1,"bind_pose": [ ],"INVERSE_BIND_POSE": [ ], "joint9": "ID": 8,"PARENT": joint1,"bind_pose": [ ],"INVERSE_BIND_POSE": [ ], "ANIMATION": "FRAME_LENGTH": 24, "FRAMES": "joint3": 1: [ ], 2: [ ], 3: [ ], 4: [ ], 5: [ ], 6: [ ], 19: [ ],20: [ ],21: [ ],22: [ ],23: [ ],24: [ ], "joint4": 1: [ ], 2: [ ], 3: [ ], 4: [ ], 5: [ ], 6: [ ], 19: [ ],20: [ ],21: [ ],22: [ ],23: [ ],24: [ ], Figure 4. Animated cube JSON model file 3.1 Static geometry The elements related to vertices, positions, normals, texture coordinates, and indices are located within the <library_geometries> element. Arnaud and Barnes [2] mention that the <library_geometries> element may contain numerous <geometry> elements. Furthermore, each <geometry> element includes a <mesh> element. The <mesh> element is the most interesting, as it holds one or more <source> elements and exactly one <vertices> element [2]. Once a <mesh> element is discovered, it must be examined for <source> elements. A typical <source> element will contain a <float_array> and a <technique_common> element. The <float_array> element s content contains a great deal of relevant data, and the <technique_common> element will hold <accessor> information for clarification. The <float_array> count attribute discloses the number of values within the array. Since a <mesh> may contain more than one

3 <source> element, the <source> id attribute must be checked against the <input> children of the appropriate parent element. As an example of the fact that the data for a single element is scattered throughout the COLLADA tree hierarchy, sometimes with logical pointers from one portion of the tree into another, the parent element for position is the <vertices> element, and it is necessary to compare the source attribute of the <input> child of <vertices> that has a semantic attribute equivalent to POSITION with the id attribute from the proposed <source> element. If the two attributes match, then the <source> element actually does contain vertex position information. For normals and texture coordinates, the <source> id attribute must be matched to an <input> source attribute within <triangles> instead of <vertices>. The <triangles> element links to the texture value for the texture coordinates with its material attribute, and the actual indices are stored within the <p> child of the <triangles> element. An <input> child of the <triangles> element with a VERTEX semantic requires an extra step, as its source attribute points back to the <vertices> element. The <input> child of the <vertices> element will be the final reference to the positions array. The offset attributes give starting points for each <input> element s indices. 3.2 Skeletal animation data Skeletal animation data can be divided into three major parts: joints, weights, and animation frames. The joint names are located within the <library_controllers> element. The <library_controllers> element will contain one or more <controller> elements with a <skin> element. Each joint needs an inverse bind matrix to correctly represent its location [5]. The inverse bind matrices can be extracted from the same <skin> element that contains joint names. The <joints> element should be searched for an <input> with a semantic attribute of INV_BIND_MATRIX. This <input> source attribute points to a <source> that contains a <float_array> element. The <float_array> contains 16 times the number of joints, which represents a 4x4 matrix for each joint. The information in <float_array> will ultimately be stored as separate 4x4 matrices for each joint. An initial transformation for each joint and a skeleton hierarchy must be determined. Within the <library_visual_scenes> element, a <visual_scene> element will represent joint information as a <node> with a type attribute of JOINT. The id attribute of each found joint should match a name in the relevant <Name_array> element. The first joint <node> found will be considered a root joint, which means the joint has no parent and is not influenced by other joints. Every joint found may have <node> children with JOINT types. Any child joint <node> will have the current parent <node> as its skeleton parent. Each joint <node> should also contain a <matrix> element. The <matrix> element represents a 4x4 initial transformation matrix. Figure 5 depicts a skeleton hierarchy for the cube in Figure 3 where joint1 is the parent of 8 other joints. <?xml version="1.0" encoding="utf-8"?> <COLLADA xmlns="" version=""> <asset></asset> <library_visual_scenes> <node name="joint1" id="joint1" type="joint"> <matrix></matrix> <node name="joint2" id="joint2" type="joint"> <matrix></matrix> <node name="joint9" id="joint9" type="joint"> <matrix></matrix> </library_visual_scenes> <scene></scene> </COLLADA> Figure 5. Joint hierarchy and initial transformation matrices <?xml version="1.0" encoding="utf-8"?> <COLLADA xmlns="" version=""> <asset></asset> <library_controllers> <bind_shape_matrix> </bind_shape_matrix> <source id="cubecontroller-joints"> <Name_array id="cubecontroller-joints-array" count="9"> joint1 joint2 joint3 joint4 joint5 joint6 joint7 joint8 joint9 </Name_array> </source> <source id="cubecontroller-weights"> <float_array id="cubecontroller-weights-array" count="17"> </float_array> </source> <vertex_weights count="8"> <input semantic="joint" offset="0" source="#cubecontroller-joints"/> <input semantic="weight" offset="1" source="#cubecontroller-weights"/> <vcount> </vcount> <v> //vertex //vertex //vertex //vertex //vertex //vertex //vertex //vertex 7 </v> </vertex_weights> </library_controllers> <scene></scene> </COLLADA> Figure 6. Weights and bind shape matrix

4 Inside the same <controller> element that contains joint information, weight information can also be found. First, a <bind_shape_matrix> element contains a 4x4 matrix that allows for the mesh to be transformed by the skeleton s coordinate system [2]. Next, a single <vertex_weights> contains <input> elements labeled with the semantic attributes JOINT and WEIGHT. The source attribute of the JOINT <input> should match the source attribute associated with the corresponding joint names, while the WEIGHT <input> points to a new <source> element. That <source> has a <float_array> child that contains all possible weights for the skin. Figure 6 shows the weight information for the skinned animated cube. All information for animation frames is located in the <library_animations> element. This element contains an <animation> element for each animated joint. The name attribute for each <animation> ties it to a specific joint. There is an <input> for a <sampler> for each <animation> that has an OUTPUT semantic attribute with a source attribute that points to a <source> element containing animation transform matrices. That <source> element contains a <float_array> with a count attribute equal to 16 times the number of frames since there are 16 elements in each frame matrix. Figure 7 shows a <library_animations> element for joint3 with all but the first two frames (32 elements) of the float arrays removed for readability. The joint joint3 is animated for 24 frames in this example, so there are 384 values total. <?xml version="1.0" encoding="utf-8"?> <COLLADA xmlns="" version=""> <asset></asset> <library_animations> <animation id="joint3-anim" name="joint3"> <animation> <source id="joint3-animation-output-transform"> <float_array id="joint3-matrix-animation-outputtransform-array" count="384"> </float_array> </source> <sampler id="joint3-animation-transform"> <input semantic="output" source="#joint3-animationoutput-transform" /> </sampler> </animation> </animation> </library_animations> <scene></scene> </COLLADA> Figure 7. Animation frame data for joint3 4 Python for COLLADA to JSON elementtree is a Python wrapper that allows the programmer to load XML files and store them as trees of elements. These trees can then be easily searched for the needed information. Figure 8 shows four examples of the simplicity and power of elementtree. The find method returns the first child of the current element, while findall returns all direct children of the current element. Using / specifies the path to the descendant element of the current element, while []'s can be used to specify attributes. For example #1 in Figure 8 will find the first <input> child of the <triangles> child of the current <mesh> that has a semantic attribute of VERTEX. A // can be used to search the entire subtree of the current element. For example #2 in Figure 8 will find all <node>'s that are descendants of <visualscene> while example #3 will find all <nodes>'s of type JOINT that are descendants of <visualscene>. Example #4 will return the first <material> descendant of the <library_materials> child of <root> that has an id of materialname. 1. vertexpossrc = mesh.find("./triangles/input[@semantic='vertex']") 2. allnodes = visualscene.findall(".//node") 3. jointnodes = visualscene.findall(".//node[@type='joint']") 4. material = root.find("./library_materials//material[@id='%s']" % (materialname) ) Figure 8. Sample elementtree code for extracting data from XML After the data has been extracted, it may have to be massaged in up to three different ways. First, each matrix extracted from the COLLADA file must be converted from row-major to column-major order. Second, since WebGL can only utilize a single index array, the separate position, normal, and texcoord arrays from the COLLADA file must be altered [3][7]. This index mapping for positions, normals, and texcoords works by examining inline indices in groups of three. For example, if the first indices examined were 3, 0, and 3, then the three elements in the third row of the COLLADA position array should be written to the JSON position array, the three elements in row 0 of the normal array should be written to the JSON normal array, and the two elements of the texcoord array found in row 3 should be written to the JSON texcoord array. The final index for all of these values is now stored as 0. This method is continued with increasing final indices until a repeating group of three original indices is encountered. Third, each vertex can have zero to n direct joint influences, so weight padding is required. Since WebGL will read a single weight array sequentially, zero weights must be appended to all vertices until they are associated with n weights. In our example n = 3. 5 WebGL There are four major steps for rendering a JSON model: initializing the WebGL context, compiling the shader program, pushing content from JSON to the GPU, and finally starting the rendering loop. In this paper we will not discuss initializing the WebGL context or the rendering loop as they are basic techniques described in [3] that are independent of what you might be rendering. The other two steps described in

5 this section build on techniques written by Rowell [9], Thomas [11], and Seidelin [10]. Rowell s base code was augmented to support skeletal animation [9]. 5.1 Shader program WebGL uses a subset of the OpenGL Shading Language for rendering known as GLSL ES [3]. Cantor and Jones [3] explain that GLSL ES is a lightweight, C-like language with specialized facilities for handling vectors and matrices. A shader program, consisting of a vertex and fragment shader, is required for rendering [1]. Anyuru [1] goes on to mention that a vertex shader handles geometric data one vertex at a time. The resulting information is converted to fragments and passed to the fragment shader; each fragment has the potential to ultimately become a pixel on the screen [1]. A major goal of this project was to support skeletal animation and basic lighting, which requires more complex shaders. New attributes for normals, joint identifiers, and joint weights must be sent to the vertex shader. Additionally, each vertex uses extra uniforms for all joint transform matrices, a normal matrix, and lighting information. A new varying variable for light weighting is also passed to the fragment shader. Figure 9 shows a commented and extensively altered fragment of a vertex shader for skeletal animation and lighting. 5.2 JSON to GPU Once the shader program has been initialized, data can be accessed from the JSON model and sent to the shaders. First the IMAGE_LOCATION is used to a load the texture image; the image must finish loading before any information is pushed to the GPU (Figure 10 shows how to initialize a texture). Next the POSITION, NORMAL, TEXTCOORD, JOINT_ID, WEIGHT, and INDEX arrays from the JSON model must be put into buffers for the vertex shader (see Figure 11). After the texture has loaded and the buffers have been filled, they can be pushed to the GPU. This requires setting up a vertex attribute pointer and binding each buffer [9] (Figure 12). The final step before drawing the scene is setting the uniforms based on the current projection, modelview, normal, and joint matrices (Figure 13). The projection, model-view, and lighting uniforms only need to be updated when the perspective changes, the camera moves, or the model is transformed, so they do not need to be updated for every frame. Since the joint matrices are meant for animation, they have the potential to change for each frame and should be handled differently than the other uniforms. To calculate the joint matrices, a float array of size 16 times the maximum number of joints should be populated with JSON data. Every joint has a name, parent name, bind matrix, and inverse bind matrix in the JSON file. Since a joint can influence other joints, a set of world joint transformations must be calculated. A joint s world matrix is equal to the product of its parent s world matrix and its own bind pose matrix; if a joint has no parent, its world matrix is simply its own bind pose matrix. A joint s world matrix is then multiplied by its inverse bind matrix and the skin s bind shape matrix. The resulting 4x4 matrix can then be stored before being sent to the shader. If the model has associated animations, then the current frame s joint matrix takes the place of the joint s bind pose matrix for world matrix calculation. Figure 14 gives pseudocode for calculating the skinning and animation matrices for joints. attribute vec3 avertexposition; //positions x,y,z attribute vec3 avertexnormal; //normals x,y,z attribute vec3 ajointid; //joint ids padded to 3 attribute vec3 ajointweight; //joint weights padded to 3 uniform mat4 ujmatrix[30]; //up to 30 4x4 joint matrices uniform mat4 umvmatrix; //4x4 model-view matrix uniform mat4 upmatrix; //4x4 projection matrix uniform vec3 ulightingdirection; //light direction void main(void) vec4 newvertex; //vertex after joint transformations vec4 newnormal; //normal after joint transformations //if no joint influences still render the vertex //calculate the new vertex based on the corresponding joint matrices newvertex = ujmatrix[int(ajointid[0])] * vec4(avertexposition, 1.0) * ajointweight[0]; newvertex = ujmatrix[int(ajointid[1])] * vec4(avertexposition, 1.0) * ajointweight[1] + newvertex; newvertex = ujmatrix[int(ajointid[2])] * vec4(avertexposition, 1.0) * ajointweight[2] + newvertex; newvertex[3] = 1.0; //calculate the new normal based on the corresponding joint matrices newnormal = ujmatrix[int(ajointid[0])] * vec4(avertexnormal, 0.0) * ajointweight[0]; newnormal = ujmatrix[int(ajointid[1])] * vec4(avertexnormal, 0.0) * ajointweight[1] + newnormal; newnormal = ujmatrix[int(ajointid[2])] * vec4(avertexnormal, 0.0) * ajointweight[2] + newnormal; //calculate final vertex position gl_position = upmatrix * umvmatrix * newvertex; //send textcoords to frag shader //if no lighting, send frag weights of 1.0 // //calculate final normal from the normal matrix and xyz //coordinates of newnormal //set dirlightweighting to the dot product of //transformednormal and ulightingdirection or 0.0, return the //largest value //calculate light weighting and send to frag shader Figure 9. Vertex shader for skeletal animation and lighting 6 Conclusions and future work The work presented here provides a brief overview of a process for extracting the 3D skeletal animation content from a COLLADA file generated by Maya, summarizing that data in a JSON file, and rendering the JSON data with JavaScript and WebGL. The topic for this work was specifically chosen due to a lack of applicable literature on the process. It should be noted that due to the length requirements for the paper, it is impossible to give a detailed description of the entire process. Interested readers can get a more detailed description by checking out the the subversion directory (svn co vw3). The thesis

6 directory contains a detailed description of the process. The dae2json.py files are in the utils directory. A short tutorial and demo are located at While the COLLADA files used in this work were generated from Maya, we believe that the Python program would work with COLLADA files generated from other 3D content development packages such as Blender. This would provide us with a stable pipeline for extracting 3D data from any existing COLLADA file for rendering in any HTML5/WebGL browser application without altering the browser application. //The following algorithm is from [11] //creat a texture, and image, and load the image var objecttexture = glcontext.createtexture(); objecttexture.image = new Image(); objecttexture.image.src = model['cube']['image_location']; objecttexture.image.onload = function () //wait for image to load //set the texture as the current texture glcontext.bindtexture(glcontext.texture_2d, objecttexture); //flip the data along the vertical axis glcontext.pixelstorei(glcontext.unpack_flip_y_webgl, true); //upload the image to the GPU glcontext.teximage2d(glcontext.texture_2d, 0, glcontext.rgba, glcontext.rgba, glcontext.unsigned_byte, objecttexture.image); //fast image scaling up close glcontext.texparameteri(glcontext.texture_2d, glcontext.texture_mag_filter, glcontext.nearest); //fast image scaling far away glcontext.texparameteri(glcontext.texture_2d, glcontext.texture_min_filter, glcontext.nearest); //set current texture to null so the previous texture //isn t accidentally altered glcontext.bindtexture(glcontext.texture_2d, null); Figure 10. Texture initialization //function createarraybuffer(values) and function //createelementarraybuffer(values) come from //Rowell's class [10] var objectbuffers = ; //Create the position buffer objectbuffers.positionbuffer = createarraybuffer(model['cube']['position']); //Similar calls for normal, texture, joint weight, and joint id buffers //Finally create the element array buffer for indices objectbuffers.indexbuffer = createelementarraybuffer(model['cube']['index']); Figure 11. Creating data buffers //push index buffer and bind the buffer glcontext.bindbuffer(glcontext.element_array_buffer, objectbuffers.indexbuffer); //push position buffer, //bind the buffer and set the vertex attribute pointer glcontext.bindbuffer(glcontext.array_buffer, objectbuffers.positionbuffer); glcontext.vertexattribpointer( shaderprogram.vertexpositionattribute, 3, glcontext.float, false, 0, 0); //normals,joint ids, joint weights are all bound in the same manner //as positions the code has been omitted to save space //texture buffer is bound like the other data glcontext.bindbuffer(glcontext.array_buffer, objectbuffers.texturebuffer); glcontext.vertexattribpointer(shaderprogram.texturecoordattribute, 2, glcontext.float, false, 0, 0); //activate current texture, bind it, and send it to the frag shader glcontext.activetexture(glcontext.texture0); glcontext.bindtexture(glcontext.texture_2d, texture); glcontext.uniform1i(shaderprogram.sampleruniform, 0); Figure 12. Sending attributes to the vertex shader //set up pmatrix var view = 45; //vertical field of view var aspectratio = glcontext.viewportwidth / glcontext.viewportheight; var mindist = 1; var maxdist = 500; var pmatrix = mat4.create(); //empty 4x4 matrix mat4.perspective(view, aspectratio, mindist, maxdist, pmatrix); //set up mvmatrix var mvmatrix = mat4.create(); //empty 4x4 matrix mat4.idenity(mvmatrix); //no transforms yet mat4.translate(mvmatrix, [1, -5, -10]); //trans mvmatrix for x, y, z mat4.rotate(mvmatrix,.75, [0, 1, 0]); //rotate 0.75 radians for y mat4.rotate(mvmatrix,.25, [1, 0, 0]); //rotate 0.25 radians for x var lighting = true; //turn lighting on or off var lightingdirection = [-0.3, -0.3, -1.0]; //set lighting direction var lightingcolor = [0.1, 0.1, 0.1]; //set ambient lighting color rgb var directionalcolor = [0.9, 0.9, 0.9]; //set directional lighting rgb //normalize lighting direction var ald = vec3.create(); vec3.normalize(lightingdirection, ald); vec3.scale(ald, -1); if(lighting) //enable lighting and pass ambient lighting color to shader glcontext.uniform1(shaderprogram.uselightinguniform, true); glcontext.uniform3fv(shaderprogram.ambientcoloruniform, lightingcolor); //similarly pass directional lighting color and direction to the shader //pass pmatrix to the shader as mat4 glcontext.uniformmatrix4fv(shaderprogram.pmatrixuniform, false, pmatrix); //similarly pass mvmatrix //create and pass a normal matrix for proper lighting var normalmatrix = mat3.create(); mat4.toinversemat3(mvmatrix, normalmatrix); mat3.transpose(normalmatrix); glcontext.uniformmatrix3fv(shaderprogram.nmatrixuniform, false, normalmatrix); Figure 13. Sending uniforms to the shaders

7 function setuniformjointmatrix for(each joint) store parent name; set world_matrix to an empty 4x4 matrix; if(animation frame exists) if(not a root joint) set world_matrix to parent_world_matrix * frame_matrix; set world_matrix to frame_matrix; if(not a root joint) set world_matrix to parent_world_matrix * bind_pose_matrix; set world_matrix to bind_pose_matrix; set new_matrix to world_matrix * inverse_bind_pose_matrix; set final_matrix to bind_shape_matrix * new_matrix; store final_matrix; send all matrices to the shader; Figure 14. Psuedocode for calculating joint matrices 7 References [1] Anyuru, A Professional WebGL Programming: Developing 3D Graphics for the Web. Wrox, Chichester, UK. [2] Arnaud, R., and Barnes, M COLLADA: Sailing the Gulf of 3D Digital Content Creation. A K Peters, Wellesley, MA. [3] Cantor, D., and Jones, B WebGL Beginner s Guide. Packt, Birmingham, UK. [4] Irish, P., Möller E., and Zijdel, T requestanimationframe for Smart Animating. Oct [5] Khronos, 2012, COLLADA 3D Asset Exchange Schema. Sept [6] Khronos, WebGL Specification. Sept [7] Milivojec, M., Antolovic, I., and Rancic, D Evaluation and Visualization of 3D Models Using COLLADA Parser and WebGL Technology. In International Conference on Computers and Computing (Lanzarote, Canary Islands, Spain, May 2011), [8] Mozilla, JavaScript Reference. US/docs/JavaScript/Reference, Sept [9] Rowell, E HTML5 Canvas Cookbook. Packt, Birmingham, UK. [10] Seidelin, J HTML5 Games: Creating Fun with HTML5, CSS3, and WebGL. John Wiley and Sons. Chichester, UK. [11] Thomas, G. Learning WebGL. Sept